Introduction to Metric Currents and Applications I

I will introduce metric currents, an important generalization of manifolds that forms a compact space (roughly speaking). We will develop the theory of currents following Lang's paper, and then we will look at an interesting application: Zust proved that sufficiently regular maps from the plane into the Heisenberg Group factor through a tree.  In particular, this solves the non-embedding problem for this class of maps.